On coherent families of finite-to-one functions
P Koszmider - The Journal of symbolic logic, 1993 - cambridge.org
P Koszmider
The Journal of symbolic logic, 1993•cambridge.orgWe consider the existence of coherent families of finite-to-one functions on countable
subsets of an uncountable cardinal κ. The existence of such families for κ implies the
existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove
that coherent families exist on κ= ωn, where n∈ ω, and that they consistently exist for every
cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are
Axiom A.
subsets of an uncountable cardinal κ. The existence of such families for κ implies the
existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove
that coherent families exist on κ= ωn, where n∈ ω, and that they consistently exist for every
cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are
Axiom A.
We consider the existence of coherent families of finite-to-one functions on countable subsets of an uncountable cardinal κ. The existence of such families for κ implies the existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove that coherent families exist on κ = ωn, where n ∈ ω, and that they consistently exist for every cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are Axiom A.
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